Heat Conduction Within Linear Thermoelasticity
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| Author | : William A. Day |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 91 |
| Release | : 2013-03-07 |
| Genre | : Science |
| ISBN | : 1461395550 |
J-B. J. FOURIER'S immensely influential treatise Theorie Analytique de la Chaleur [21J, and the subsequent developments and refinements of FOURIER's ideas and methods at the hands of many authors, provide a highly successful theory of heat conduction. According to that theory, the growth or decay of the temperature e in a conducting body is governed by the heat equation, that is, by the parabolic partial differential equation Such has been the influence of FOURIER'S theory, which must forever remain the classical theory in that it sets the standard against which all other theories are to be measured, that the mathematical investigation of heat conduction has come to be regarded as being almost identicalt with the study of the heat equation, and the reader will not need to be reminded that intensive analytical study has t But not entirely; witness, for example, those theories which would replace the heat equation by an equation which implies a finite speed of propagation for the temperature. The reader is referred to the article [9] of COLEMAN, FABRIZIO, and OWEN for the derivation of such an equation from modern Continuum Thermody namics and for references to earlier work in this direction. viii Introduction amply demonstrated that the heat equation enjoys many properties of great interest and elegance.
| Author | : William A. Day |
| Publisher | : Springer |
| Total Pages | : 0 |
| Release | : 2012-01-16 |
| Genre | : Science |
| ISBN | : 9781461395577 |
J-B. J. FOURIER'S immensely influential treatise Theorie Analytique de la Chaleur [21J, and the subsequent developments and refinements of FOURIER's ideas and methods at the hands of many authors, provide a highly successful theory of heat conduction. According to that theory, the growth or decay of the temperature e in a conducting body is governed by the heat equation, that is, by the parabolic partial differential equation Such has been the influence of FOURIER'S theory, which must forever remain the classical theory in that it sets the standard against which all other theories are to be measured, that the mathematical investigation of heat conduction has come to be regarded as being almost identicalt with the study of the heat equation, and the reader will not need to be reminded that intensive analytical study has t But not entirely; witness, for example, those theories which would replace the heat equation by an equation which implies a finite speed of propagation for the temperature. The reader is referred to the article [9] of COLEMAN, FABRIZIO, and OWEN for the derivation of such an equation from modern Continuum Thermody namics and for references to earlier work in this direction. viii Introduction amply demonstrated that the heat equation enjoys many properties of great interest and elegance.
| Author | : Clifford Truesdell |
| Publisher | : Springer |
| Total Pages | : 755 |
| Release | : 2013-12-17 |
| Genre | : Technology & Engineering |
| ISBN | : 3662397765 |
| Author | : Józef Ignaczak |
| Publisher | : Oxford University Press |
| Total Pages | : 432 |
| Release | : 2010 |
| Genre | : Language Arts & Disciplines |
| ISBN | : 0199541647 |
A unique monograph in a fast developing field of generalized thermoelasticity, an area of active research in continuum mechanics, focusing on thermoelasticity governed by hyperbolic equations, rather than on a wide range of continuum theories.
| Author | : Yuriy Povstenko |
| Publisher | : Springer Nature |
| Total Pages | : 457 |
| Release | : |
| Genre | : |
| ISBN | : 3031645871 |
| Author | : Witold Nowacki |
| Publisher | : Elsevier |
| Total Pages | : 579 |
| Release | : 2013-10-22 |
| Genre | : Science |
| ISBN | : 1483162486 |
Thermoelasticity, Second Edition reviews advances in thermoelasticity and covers topics ranging from stationary problems of thermoelasticity to variational theorems of stationary thermoelasticity; stresses due to the action of a discontinuous temperature field in an infinite elastic body; the action of heat sources in the elastic space; and thermal inclusions in an infinite disc and semi-infinite disc. Three different sets of differential equations describing the fields of strain and temperature are presented. This book is comprised of 12 chapters and begins with a discussion on basic relations and equations of thermoelasticity. Thermoelasticity is treated as a synthesis of the theory of elasticity and the theory of heat conduction. Some particular cases of thermoelasticity are then investigated, including stationary problems, the theory of thermal stresses, and classical dynamic elasticity. Dynamic effects due to the action of a non-stationary temperature field are examined, along with plane harmonic waves in an elastic space and thermal stresses in plates, shells, and viscoelastic bodies. The final chapter focuses on micropolar thermoelasticity, magnetothermoelasticity, and thermopiezoelectricity. This monograph will be of interest to physicists and mechanical engineers.
| Author | : Reinhard Racke |
| Publisher | : CRC Press |
| Total Pages | : 322 |
| Release | : 2000-06-21 |
| Genre | : Mathematics |
| ISBN | : 9781584882152 |
Although the study of classical thermoelasticity has provided information on linear systems, only recently have results on the asymptotic behavior completed our basic understanding of the generic behavior of solutions. Through systematic work that began in the 80s, we now also understand the basic features of nonlinear systems. Yet some questions remain open, and the field has lacked a comprehensive survey that explores these past results and presents recent developments. Evolution Equations in Thermoelasticity presents a modern treatment of initial value problems and of initial boundary value problems in both linear and nonlinear thermoelasticity, in one- and multi-dimensional spatial configurations. The authors provide the first self-contained presentation of the subject that offers both introductory parts accessible to graduate students and sophisticated sections valuable to experts.
| Author | : Erling Fjær |
| Publisher | : Elsevier |
| Total Pages | : 515 |
| Release | : 2008-01-04 |
| Genre | : Science |
| ISBN | : 0080557090 |
Engineers and geologists in the petroleum industry will find Petroleum Related Rock Mechanics, 2e, a powerful resource in providing a basis of rock mechanical knowledge - a knowledge which can greatly assist in the understanding of field behavior, design of test programs and the design of field operations. Not only does this text give an introduction to applications of rock mechanics within the petroleum industry, it has a strong focus on basics, drilling, production and reservoir engineering. Assessment of rock mechanical parameters is covered in depth, as is acoustic wave propagation in rocks, with possible link to 4D seismics as well as log interpretation. - Learn the basic principles behind rock mechanics from leading academic and industry experts - Quick reference and guide for engineers and geologists working in the field - Keep informed and up to date on all the latest methods and fundamental concepts
| Author | : Bruno A. Boley |
| Publisher | : Courier Corporation |
| Total Pages | : 610 |
| Release | : 2012-05-23 |
| Genre | : Technology & Engineering |
| ISBN | : 0486143864 |
Highly regarded text presents detailed discussion of fundamental aspects of theory, background, problems with detailed solutions. Basics of thermoelasticity, heat transfer theory, thermal stress analysis, more. 1985 edition.
| Author | : Richard B. Hetnarski |
| Publisher | : Springer |
| Total Pages | : 657 |
| Release | : 2019-04-11 |
| Genre | : Science |
| ISBN | : 3030104362 |
This is an advanced modern textbook on thermal stresses. It serves a wide range of readers, in particular, graduate and postgraduate students, scientists, researchers in various industrial and government institutes, and engineers working in mechanical, civil, and aerospace engineering. This volume covers diverse areas of applied mathematics, continuum mechanics, stress analysis, and mechanical design. This work treats a number of topics not presented in other books on thermal stresses, for example: theory of coupled and generalized thermoelasticity, finite and boundary element method in generalized thermoelasticity, thermal stresses in functionally graded structures, and thermal expansions of piping systems. The book starts from basic concepts and principles, and these are developed to more advanced levels as the text progresses. Nevertheless, some basic knowledge on the part of the reader is expected in classical mechanics, stress analysis, and mathematics, including vector and cartesian tensor analysis. This 2nd enhanced edition includes a new chapter on Thermally Induced Vibrations. The method of stiffness is added to Chapter 7. The variational principle for the Green-Lindsay and Green-Naghdi models have been added to Chapter 2 and equations of motion and compatibility equations in spherical coordinates to Chapter 3. Additional problems at the end of chapters were added.
